A  STUDY  OF  THE  HEATS  OF  DILUTION  OF 
CERTAIN  AQUEOUS  SALT  SOLUTIONS 


BY 


ALLEN  EDWIN  STEARN 

A.B.  Stanford  University,  1915 
A.M.  Stanford  University,  1916 
M.  S.  University  of  Illinois,  1917 


THESIS 

Submitted  in  Partial  Fulfillment  of  the  Requirements  for  the 

Degree  of 
DOCTOR  OF  PHILOSOPHY 

IN  CHEMISTRY 


/ 


SB  I 


IN 


THE  GRADUATE  SCHOOL 


OF  THE 


UNIVERSITY  OF  ILLINOIS 


1919 


- 


KASTON,  PA.: 

BSCHSNBACH  PRINTING  COMPANY 
1919 


A  STUDY  OF  THE  HEATS  OF  DILUTION  OF 
CERTAIN  AQUEOUS  SALT  SOLUTIONS 


BY 


ALLEN  EDWIN  STEARN 

l! 

A.B.  Stanford  University,  1915 
A.M.  Stanford  University,  1916 
M.  S.  University  of  Illinois,  1917 


THESIS 

Submitted  in  Partial  Fulfillment  of  the  Requirements  for  the 

Degree  of 
DOCTOR  OF  PHILOSOPHY 

IN  CHEMISTRY 

IN 

THE  GRADUATE  SCHOOL 
OF  THE 

UNIVERSITY  OF  ILLINOIS 
1919 


EASTON,  PA.: 

ESCHENSACH  PRINTING  COMPANY 
1919 


ACKNOWLEDGMENT. 

I  wish  to  express  my  appreciation  of  the  suggestions  of  Dr.  G.  McP. 
Smith  under  whose  supervision  this  investigation  was  carried  on.  To  Dr. 
J.  M.  Braham  I  am  also  indebted  for  the  use  of  his  calorimeter  and  his 
suggestions  regarding  its  manipulation,  and  to  Dr.  D.  A.  Maclnnes  for 
permission  to  reproduce  his  drawings  of  the  apparatus.  Acknowledgment 
is  also  due  Mr.  R.  F.  Schneider  for  assistance  during  the  research. 


464191 


A  Study  of  the  Heats  of  Dilution  of  Certain 
Aqueous  Salt  Solutions* 


A.  Introduction. 

i.  Purpose  of  the  Investigation. — A  series  of  investigations1  under- 
taken in  this  laboratory  with  the  object  of  studying  ionic  relationships 
in  aqueous  solutions  of  mixed  strong  electrolytes  has  indicated  the  forma- 
tion of  higher  order  compounds  in  the  ionization  process,  in  harmony 
with  Werner's  ideas  in  regard  to  its  mechanism. 

The  method  of  investigation  in  the  papers  referred  to  has  been  to  study 
the  equilibria  between  aqueous  and  metallic  solutions,  using  mixed  salt 

1  G.  McP.  Smith,  Am.  Chem.  J.,  37,  506  (1907);  /.  Am.  Chem.  Soc.,  32,  502  (1910); 
35>  39  (1913);  Smith  and  Ball,  Ibid.,  39,  179  (1917);  Smith  and  Braley,  Ibid.,  39,  1545 
(1017);  40,  197  (1918);  Smith  and  Rees,  Ibid.,  40,  1802  (1918). 


solutions  and  liquid  amalgams.  The  measurement  of  some  colligative 
property  of  aqueous  solutions  seemed  to  offer  a  means  of  testing  these 
ideas  from  another  point  of  attack,  and  consequently  it  was  planned  in 
this  investigation  to  measure  the  reversible  molal  heats  of  dilution  of 
certain  mixed  salt  solutions  and  to  compare  these  with  the  heats  of  dilu- 
tion of  solutions  of  the  single  salts. 

2.  Heats  of  Dilution.  —  The  reversible  molal  heat  of  dilution,  LD, 
of  an  aqueous  solution  at  any  concentration  is  represented  by  the  differ- 
ence in  the  heats  of  vaporization  of  one  mol  of  water  from  a  solution  of 
that  concentration  and  from  pure  water. 

Thus:  LD  =  Lv  --  Lv. 

Here  LD  is  the  reversible  molal  heat  of  dilution,  Lv  is  the  heat  of  vapor- 
ization of  one  mol  of  water  from  the  solution  in  question,  and  Lv  is  the 
heat  of  vaporization  of  one  mol  of  water  from  pure  water. 

But 


dT 


Or  _  d  In  P/p0 

LD  -  Kl          dT      . 

Without  a  large  mass  of  experimental  data  on  the  partial  vapor  pressure 
of  water  in  solutions  of  various  concentrations  and  at  various  temperatures, 
there  is  no  method  of  calculating  the  value  of  LD  without  assuming 
Raoult's  law  for  cases  for  which  we  know  it  does  not  hold.  For  dilute 
solutions  where  Raoult's  law  does  hold  the  ratio  p/p0  approaches  unity 
so  that  LD  is  zero.  In  concentrated  solutions,  however,  "or  in  dilute 
solutions  where  the  process  of  dilution  is  associated  with  the  formation 
of  new  molecular  complexes,  or  with  the  decomposition  of  those  already 
occurring,  the  heat  of  dilution  may  have  a  positive  or  negative  value."2 

If,  now,  one  should  measure  the  reversible  molal  heat  of  dilution  for  a 
given  concentration  of  solutions  of  single  salts,  and  then  for  an  equiva- 
lent concentration  of  a  solution  of  the  mixed  salts,  one  might  expect  to 
find  the  value  in  the  latter  case  to  be  somewhere  near  the  sum  of  the  other 
values  unless  affected  by  the  formation  of  new  molecular  complexes. 

B,  Materials. 

The  strontium  chloride  was  in  the  form  of  "pure  crystals."  Most  of 
the  material  was  recrystallized  once  from  water.  This  procedure  in  the 
light  of  our  results  seems  unnecessary  when  it  is  considered  that  the  heat 
effects  in  solutions  as  concentrated  as  0.2  N  are  so  small  as  to  be  hardly 
measureable.  The  sodium  and  potassium  chlorides  were  of  various 
brands,  all  labeled  c.  P.  These  materials  are  easy  to  obtain  in  a  state  of 
high  purity,  and  inasmuch  as  small  amounts  of  impurities  have  no  effect 

1  Kirchhoff,  Pogg.  Ann.,  104  (1856);  Ges.  Abh.,  p.  492. 

2  Nernst,  "Theoretical  Chemistry,"  Trans.  6th  Ger.  Ed.,  p.  143. 


on  the  results  in  this  work,  it  was  considered  unnecessary  to  purify  them 
further. 

C.  Apparatus. 

The  apparatus  was  a  very  slight  modification  of  the  adiabatic  calorim- 
eter of  Maclnnes  and  Braham.1  The  instrument  itself  was  that  actually 
employed  by  Braham,  as  were  the  thermometers,  Wheatstone  bridge, 
standard  cells,  etc. 

A  calorimetric  determination  of  a  positive  heat  effect  consisted  of 
measuring  the  change  in  resistance  of  a  coil  of  platinum  wire  due  to  the 
direct  dilution  of  a  certain  quantity  of  solution  of  a  certain  concentra- 
tion with  a  certain  quantity  of  water.  Next,  a  carefully  measured  quan- 
tity of  electrical  energy  was  introduced  into  the  solution  and  the  corre- 
sponding change  in  resistance  of  the  same  coil  measured.  For  negative 
heats  a  slightly  different  procedure  was  followed  where  these  heats  were 
comparatively  large.  In  such  cases  the  procedure  was  to  introduce  elec- 
trical energy  into  the  solution  at  a  carefully  measured  rate  slightly  more 
rapidly  than  it  was  taken  up  in  dilution,  so  that  the  solution  did  not  cool 
down  below  the  temperature  of  the  surroundings.  The  reason  for  this 
is  that  it  is  much  easier  to  adjust  the  surroundings  to  a  rising  tempera- 
ture in  the  calorimeter  by  means  of  heating  coils,  than  to  a  decreasing 
temperature  in  the  calorimeter  where  the  cooling  of  the  surroundings  could 
not  be  closely  regulated  with  any  degree  of  satisfaction.  After  finishing 
the  run  as  described  above,  one  can  calculate  the  number  of  calories  cor- 
responding to  the  electrical  energy  introduced,  and  the  actual  number 
of  calories  corresponding  to  the  increase  in  temperature  as  measured  by 
the  change  in  resistance  of  the  thermometer.  The  difference  is  the  num- 
ber of  calories  due  to  the  heat  of  dilution.  By  this  procedure  the  heat 
capacity  of  the  calorimeter  is  measured  as  a  part  of  every  determina- 
tion, and  thus  inaccuracies  due  to  calculations  from  questionable  data 
on  specific  heats  of  solutions,  water  equivalent  of  the  calorimeter,  slightly 
varying  conditions  of  the  experiments,  uncertainties  arising  from  the 
calibration  of  the  thermometer,  etc.,  are  eliminated.  Thus  by  a  simple 
proportion  the  heat  of  dilution  can  be  obtained  at  once.  For  if  HD  is 
the  heat  due  to  dilution,  expressed  in  joules,  then 

HD  :  EIT  =  RD  :  RE, 

where  E  is  electromotive  force,  /  the  current,  and  T  the  time  in  seconds 
during  which  the  current  is  passed  through  the  calorimeter  heater.  RD 
and  RE  are  the  changes  in  temperature,  in  resisting  units,  due,  respec- 
tively, to  the  dilution  and  to  the  electrical  heating. 

—  HD  (in  calories) :  — —  =  RD  '  RE 

where  J  represents  Joule's  equivalent,  4.184  joules  per  calorie. 
1  Maclnnes  and  Braham,  /.  Am.  Chem.  Soc.,  39,  2110  (1917)- 


8 

Since  the  relation  between  the  change  in  resistance  and  the  tempera- 
ture change  is  not  linear,  any  large  values  of  RD  or  RE  would  have  to  be 
corrected  by  means  of  the  relation 


100          100' 

in  which  -Rioo  is  the  resistance  of  the  thermometer  in  steam  at  760  mm. 
pressure,  RQ  is  its  resistance  in  melting  ice,  and  d'  is  an  empirical  constant. 
Maclnnes  and  Braham  determined  RIOO  and  R0  for  the  thermometers 
employed,  and  used  for  d'  the  value  1.47,  recommended  by  the  Bureau 
of  Standards.  They  found,  however,  that  with  the  values  of  RD  and  RE 
of  the  magnitude  met  with  in  their  work,  which  were  even  greater  than 
those  met  with  in  this  investigation,  the  correction  was  too  small  to  affect 
their  numerical  results  in  any  way;  so  that  if  AR  =  0.02395,  then  At  = 
0.2395,  just  10  times  the  numerical  value  of  &R. 

D.  Method. 

The  salt  solutions  were  made  on  the  basis  of  gram  equivalents  of  an- 
hydrous salt  per  1000  g.  of  water.  Their  concentration  was  ascertained 
by  a  Volhard  determination  of  the  chlorine.  The  salts  used  were  sodium 
chloride,  potassium  chloride  and  strontium  chloride;  and  the  concentra- 
tions at  which  the  heats  of  dilution  were  determined  were  0.2,  0.4,  0.8, 
1.6  and  3.2  weight  normal.1  Points  on  the  strontium  chloride  curve  were 
also  obtained  for  concentrations  of  1.2,  2.0,  2.4  and  2.8  wt.  N.  Mixed 
salt  solutions  of  NaCl  :  l/2  SrCl2,NaCl  :  KC1,  KC1  :  l/2  SrCl2,  and  KC1  : 
SrCl2  were  also  run  at  the  above  mentioned  concentrations.  These  solu- 
tions were  prepared  by  diluting  a  volume  of  the  solution  of  one  of  the  salts 
with  an  equal  volume  of  the  solution  of  the  same  concentration  of  the 
other  salt.  Thus  one  volume  of  0.8  wt.  N  potassium  chloride  and  one 
volume  of  0.8  wt.  N  sodium  chloride  were  mixed  and  called  0.8  wt.  N 
of  the  mixed  salt. 

The  value  of  the  reversible  molal  heat  of  dilution  was  obtained  by  di- 
luting the  solution  of  a  definite  concentration  with  decreasing  amounts  of 
water,  and  plotting  the  heat  effects  obtained  against  the  number  of  mols 
of  water  added.  The  curve  was  found  to  be  a  straight  line  (within  this 
region)  so  that,  by  extrapolation  to  zero  mols  of  water  added,  the  value 
of  the  reversible  molal  heat  of  dilution  at  the  particular  concentration 
could  be  obtained. 

Accuracy. — The  very  small  values  of  the  heat  effects  in  the  case  of 
the  more  dilute  solutions  necessitated  only  approximate  results  here. 
Maclnnes  and  Braham  state  that  heat  effects  of  from  50  to  60  calories 

1  Weight  normal  or  wt.  N  is  the  number  of  gram  equivalents  of  anhydrous  salt 
per  1000  g.  of  water. 


-30 

r 

\ 

_       Vpptr  Curve.-  3./6  /nob  tfCt 

\ 

\ 

0 

^ 

i^ 

!' 

x. 

^ 

—3 

*< 

-- 

IOO      ISO 
Water    of   Di\ui.ion 


can  be  measured  with  an  accuracy  of  from  4  to  5%.*  With  a  total  heat 
effect  of  from  5  to  20  calories  one  should  not  expect  much  more  than  30 
to  50%  accuracy.  In  these  cases,  however,  an  error  of  even  100%  would 
change  the  point  on  the  curve  of  the  concentration  plotted  against  the 
molal  heat  effect  to  such  a  slight  extent  that  the  curve  itself  would  be 
unaffected.  In  the  case  of  the  larger  heat  effects,  running  as  high  as 
600  to  700  calories,  the  heat  change  can  be  measured  to  within  0.25  to 
0.5%,  so  that  the  error  of  the  reversible  heat  value  should  not  be  greater 
than  i  to  2%. 

Some  justification  for  the  assumption  that  the  molal  heat  values  ob- 
tained by  diluting  a  certain  quantity  of  solution  with  varying  amounts  of 
water  give  a  straight  line  when  plotted  against  the  number  of  mols  of 

water  of  dilution  is  given  in  Fig.  i. 
The  data  for  these  curves  are  taken 
from  Tables  IV  and  VII.  Accord- 
ing to  Thomsen2  "the  value  of  the 
thermal  change  on  dilution  always 
varies  with  variations  in  the  quantity 
of  water  of  dilution,  and  this  varia- 
tion, whether  positive  or  negative, 
seems  to  have  the  character  of  a 
hyperbolic  function  of  the  quantity 
of  water  added."  As  will  be  seen, 
the  region  of  the  curve  on  which  the 
experimental  data  represented  in  all  the  subsequent  curves  fall  is  so  far 
from  the  vertex  that  the  change  of  slope  of  the  curve  has  become  vanish- 
ingly  small,  and  it  is  practically  a  straight  line.  (In  Fig.  i ,  mols  of  water 
of  dilution  per  10,000  g.  of  solution  are  plotted  as  abscissas,  and  the  molal 
heat  effects  as  ordinates.) 

E.  Experimental  Results. 

Tables  I  to  VIII  give  the  data  for  the  heats  of  dilution  of  various  salt 
solutions  and  mixtures.  Table  I  gives  in  considerable  detail  the  results 
of  a  run  including  resistance  readings,  results  of  potentiometer  readings, 
etc.  Table  I  is  for  the  case  of  a  negative  heat  effect,  and  a  sample  calcu- 
lation from  the  data  included  in  the  table  is  appended. 

In  this  table,  "Time"  is  the  time  in  seconds  during  which  heat  is  passed  through 
the  calorimeter  heater;  "Res."  is  the  resistance  of  the  thermometer  in  ohms;  "R" 
is  the  change  of  resistance  of  the  thermometer  in  ohms  multiplied  by  io5;  "Sol.  G." 
represents  the  number  of  grams  of  solution  to  be  diluted;  "Mols  H2O"  represents  the 
number  of  mols  of  water  (assuming  18  g.  to  the  mol)  with  which  the  solution  was  diluted; 

1  It  may  be  stated  that  to  measure  the  change  of  resistance  due  to  dilution  or  to 
the  electrical  energy  passed  into  the  calorimeter  it  was  not  necessary  to  shift  a  plug  in 
the  resistance  box. 

2  Pattison  Muir,  "Elements  of  Thermal  Chemistry,"  p.  167. 


Fig.  i. — Change  of  molal  heat  effect  with 

the  number  of  mols  of  water  of 

dilution  over  a  wide  range. 


10 


"Amp."  is  the  current  in  amperes  through  the  heating  coil  of  the  calorimeter;  "E.  M. 
F."  is  the  voltage  drop  across  the  terminals  of  this  same  coil;  "Cal."  is  the  number  of 
calories  of  electrical  energy  introduced. 

The  total  heat  effect  of  the  dilution  is  given  in  calories  as  well  as  the 
molal  heat  effect.  The  latter  value  is  obtained  from  the  former  by  dividing 
it  by  the  number  of  mols  of  water  of  dilution. 

A  few  curves  representative  of  the 
method  of  extrapolation  are  given. 
Mols  of  water  of  dilution  are  plotted 
as  abscissas  and  molal  heat  effects  as 
ordinates.  Fig.  2  gives  the  curve  for 
2.9  wt.  N  SrCl2  and  that  for  0.8  wt.  N 
KC1.  The  size  of  the  plotted  point 
gives  an  estimate  of  the  probable  ac- 
curacy of  each  point.  The  radius 
of  the  circle  represents  the  variation  in 
the  molal  heat  of  dilution  due  to  a 
variation  of  o.ooooi  ohm  in  the  re- 
sistance measurement.  In  the  remainder  of  the  data,  the  values  obtained 
by  drawing  similar  curves  are  given  but  the  curves  themselves  are  not 
included. 

Tables  III  to  IX  give  a  condensed  summary  of  some  50  tables  of  the 
type  of  Table  I. 

I. — HEAT  OF  DILUTION  OF  3.2  WT.  N  NaCl. 


IS       20       2o       50 
W<aier    of  Di/ut./on 


Fig.  2.  —  Molal  heat  effect  as  a  function 

of  the  amount  of  water  of  dilution. 

(NOTE  :   Read  the  ordinates  as  negative 

for  the  NaCl  curve.) 


Time. 
Sec. 


300 


300 


300 


300 


300 


300 


Res.   d 
Ohms. 

27.41500 
3205 

3875 

5190 

27.43500 

2795 

3605 

4865 

27.44500 
2862 

3808 
5043 


X  105. 
Ohms. 


670 


1315 


810 


1260 


946 


1235 


Sol. 
G. 


H20. 
Mols. 


Free 
Current.   E.  M.  F.  energy. 


Amp.       Volts.         Ca 


Total  ht. 

effect. 

Cal. 


Heat 

effect 

per  mol. 

Cal. 


10,586      27.4 


2.322     6.635 


105 


10,586     18.45 


10,586        I  I  . 22 


2.305       6.58  IOQ9 


2-335     6.66       1115 


2.334     6.66       1115 


2-33       6.65 


2-335     6.66       1115 


—546     —19-9 


—398     — 21.6 


Reversible  Molal  Heat  of  Dilution, 


— 258     — 22  . 
— 25.0  cal. 


Sample  Calculation.     If  1115  cals.  produce  a  change  in  resistance  of  1235  units, 


1 1 


then  1 1 1 1  cals.  would  produce  in  the  same  amount  of  the  same  .solution  a  change  of 
resistance  of  1231  units.  The  change  measured,  however,  was  only  946  units.  A 
quantity  of  heat,  therefore,  equivalent  to  that  represented  by  a  change  of  resistance  of 
123 1  minus  946  or  285  units  was  used  up  by  dilution.  Therefore  if  1235  units  are  equiv- 
alent to  1115  cals.,  285  units  would  be  equivalent  to  258  cals.  This  value,  then,  would 
represent  the  heat  effect  due  to  dilution  with  11.22  mols  of  water.  The  molal  heat 
effect  would  then  be  258  divided  by  11.22,  or  22.95  cals.  The  sign  would,  of  course, 
be  negative. 

TABLE  II. — HEAT  OF  DILUTION  OF  NaCl  SOLUTIONS. 


Reversible 

Concen- 

Water of 

Total  heat 

Molal  heat 

molal  heat 

tration. 

Solution.              dilution. 

of  dilution. 

of  dilution. 

of  dilution. 

Wt.  N. 

G.                         Mols. 

Cal. 

Cal. 

LD  cal. 

3-2 

10,586                27.4 

-546 

—  19  9 

18-45 

—398 

21.6 

II  .22 

—258 

—22.95 

—25.0 

1.6 

8,280                   34.83 

—245 

—  7.04 

22.06 

—  179 

—8.06 

n-75 

—  IO2 

—8.67 

7-83 

7I-I 

—9.08 

—9.80 

0.8 

7,986             36-45 

7O.O 

—1.92 

32-86 

—77-8 

—  2.37 

25.65 

—70.9 

—2.76 

16-75 

—  48  •  44 

—2.89 

—3-93 

0.4 

7,900             37-72 

—  29.62 

—  0.79 

25-58 

—24.09 

—  0.94 

21.5 

—25.38 

—  1.18 

16.5 

—21.15 

—1.28 

12.47 

—  17.16 

—1.38 

8.86 

—12.48 

—1.41 

—1.  60 

O.2 

9,300              28.8 

—  17.64 

—  0.61 

23-4 

—17.9 

—  0.765 

18.  ii 

—13-4 

—0-74 

14.6 

—  10.0 

—  0.69 

—  0.85 

TABLE  III.  —  HEAT  OF 

DILUTION  OF 

KC1  SOLUTIONS. 

Reversible 

Concen- 

Water of 

Total  heat 

Molal  heat 

molal  heat 

tration. 

Solution.              dilution. 

of  dilution. 

of  dilution. 

of  dilution. 

Wt.  N. 

G.                      Mols. 

Cal. 

Cal. 

LD  cal. 

3-16 

8,410                39.0 

—781.0 

20  .  03 

26.55 

—604  .  3 

22  .  76 

19  4 

—484.0 

—24  94 

14.4 

382  .  2 

—26.48 

94 

26l  .2 

27.79 

—  30.0 

1.6 

8  ,  ooo             40  .  o 

—289.5 

—7.24 

30.0 

—  246  .  7 

—8.22 

20.0 

—177.2 

—8.87 

10.  0 

—103.3 

10.33 

10.  80 

0.8 

8  ,  ooo             40  .  o 

—70  .  68 

—i   77 

30.0 

—64.9 

—2.16 

20.  o 

—48.8 

—2.44 

IO.O 

—27.8 

—2.78 

—3-30 

12 


TABLE  III  (continued). 


Reversible 

Concen- 
tration.           Solution. 
Wt.  N.                   G. 

Water  of 
dilution. 
Mols. 

Total  heat 
of  dilution. 
Cal. 

Molal  heat 
of  dilution. 
Cal. 

molal  heat 
of  dilution. 
LD  cal. 

0.4               8  ,  ooo 

34-95 

—15  o 

—0-43 

30.0 

—  13    42 

—0-45 

25  o 

—  I4.I 

-0-564 

20.0 

—  12.44 

—  O.622 

15.0 

—  IO.O 

—  0.67 

—0.95 

0.2                    7,850 

40.0 

—2.74 

—0.069 

38-2 

2  .92 

—  o  .  076 

34-0 

—2-32 

—0.094 

30.0 

—3-1 

—  o.  103 

30.0 

—3-25 

—  o.  108 

—  o.  24 

TABLE  IV. — HEAT  OF  DILUTION  OF  SrCl2  SOLUTIONS. 


Reversible 

Concen- 
tration. 
Wt.  N. 

Solution. 
G. 

Water 
of  dilution. 
Mols. 

Total  heat 
of  dilution. 
Cal. 

Molal  heat 
of  dilution. 
Cal. 

molal  heat 
of  dilution. 
LD  cal. 

3-2 

10,000 

35-0 

189.0 

5-4 

15-0 

95-7 

6-4 

7-2 

2.9 

9,500 

37-2 

129.8 

3-49 

30.0 

I  12  .4 

3-75 

30.0 

II4.I 

3-8o 

27-7 

109.2 

3  95 

20.  o 

86.33 

4-3i 

19.5 

85-44 

4-38 

IO.O 

48-5 

4-85 

5  40 

2-4 

IO,OOO 

35-0 

33-7 

.     0.96 

25-0 

32-5 

1.29 

2.  10 

2.0 

IO,OOO 

35-0 

35-5 

i  .01 

25.0 

31.0 

1.23 

i-75 

i-55 

10,000 

40.0 

23.64 

0-59 

30.0 

21.4 

0.71 

30.0 

20.92 

0.70 

20.  o 

17-3 

0.86 

i  .  ii 

1.2 

10,000 

35-0 

18.9 

0-54 

25-0 

16.3 

0.65 

0.90 

0.8 

10,000 

40.0 

15-4 

0.38 

30.0 

13.0 

0.44 

20.0 

IO.O 

0.50 

0.62 

0.425 

10,000 

4O.O 

11.16 

0.28 

30.0 

10.07 

0-34 

20.0 

7-4 

o.37 

0.50 

0.2 

10,000 

4O.O 

7.88 

O.2O 

30.0 

6.81 

0.23 

20.0 

4.0  + 

0.2  + 

0.25  = 

TABLE  V. — HEAT  OF  DILUTION  OF  NaCl  :  KC1  SOLUTIONS. 


Concen-                              Water  of 
tration.     Solution.          dilution. 
Wt.  N.           G.                 Mols. 

Total  heat       Molal  heat 
of  dilution.        of  dilution. 
Cal.                       Cal. 

3.2         10,000        40.0 

—  780  .  o 

—19-5 

30.0 

—  658.0 

—21.9 

2O.  O 

—  468  .  0 

—23-4 

IO.O 

—  256.0 

-25-6 

1.6         10,000         40.0 

—286.6 

—7.16 

30.0 

—230.7 

—7.70 

20.0 

—  165.  I 

—8.30 

IO.O 

—88.6 

—8.86 

0.8          10,000         40.0 

—58.54 

—  i  .46 

30.0 

—52-6 

—  1-75 

20.0 

—39-25 

—1.96 

IO.O 

—23-8 

—2.38 

0.4         10,000         35.0 

21  .O 

—  0.60 

25.0 

—  16.0 

—  0.65 

15.0 

—  10.4 

—0.70 

—27.8 


20.6 


—9.40        —7-13 


—2.60        —2.55 


77  —i. 01 


0.2°       10,000         40.0  — 7.2  — o.i  8 

30.0  —58  0.19  0.2  0.55 

a  Another  run  gave  a  non-measurable  result  probably  due  to  the  fact  that  equi- 
librium between  the  solution  and  the  dilution  water  had  not  been  reached. 


TABLE  VI.— HEAT  OF  DILUTION  OF  NaCl  :  1/2  SrCl2  SOLUTIONS. 


Concen-                             Water  of 

Total  heat 

Molal  heat  Reversible  molal  heat  of  dil. 

tration.     Solution.          dilution. 
Wt.  N.           G.                 Mols. 

of  dilution. 
Cal. 

of  dilution.       -  —  •-• 
Cal.                  Obs. 

Calc. 

3.2           IO,OOO          40 

.0 

—303 

.0 

—7 

-58 

30 

.0 

-246 

.6 

—8 

.22 

20 

.0 

—  177 

.0 

—8 

•85 

10 

.0 

—95 

.0 

—9 

.50            —  IO.2O 

—  8.70 

1.6         10,000         40 

.0 

—i  08 

.8 

2 

.72 

30 

.0 

—93 

.8 

—3 

•13 

20 

0 

—70 

.2 

—3 

•51 

10 

.0 

—36 

.6 

—3 

.65            —4.20 

—3-30 

0.8          10,000         40 

.0 

—28 

.2 

—  o 

.70 

30 

o 

—  25 

•  7 

—  o 

.86 

15 

0 

—  16 

.  i 

I 

.07           —1.30 

—  1.18 

0.4         10,000         40 

0 

—8 

•65 

—o 

.22 

20 

0 

—6 

.0 

—  o 

.  30          —  o  .  40 

—  0.60 

O.2              IO,OOO             40 

0 

—5 

.0 

—o 

.  12 

25 

.0 

—3 

.0 

—  o 

.12               O.I 

—  0.2 

H 
TABLE  VII. — HEAT  OF  DILUTION  OF  KC1  :  1/2  SrCl2  SOLUTIONS. 

Reversible  molal  heat  of  dil. 
Obs.  Cals. 


Concen- 
tration. 
Wt.  N. 

Solution. 
G. 

Water  of 
dilution. 
Mols. 

Total  heat 
of  dilution. 
Cal. 

Molal  heat 
of  dilution. 
Cal. 

3-2 

10,000 

40.0 

—  575-0 

—14-37 

30.0 

—472.0 

—  15-70 

2O.  O 

—343  -  5 

—17.2 

10.  0 

—  189.0 

—  18.9 

—20.5         —9.7 

(Duplicate  Run) 

3.2         10,000 

25.0         — 412.0  — 16.48 

—20.7 
1.6         10,000 


35-0 

—514-8 

—  14.72 

25.0 

—  412.0 

—16.48 

15.0 

—  269.3 

—  17-95 

40.0 

—168.5 

—4.21 

30.0 

—  142.0 

—4  75 

20.  o 

IO2  .O 

—  5-io 

10.  0 

—54-3 

—5-43 

—  6  .  o  —  2  .  6 
(Duplicate  Run) 

1.6  10,000  35.0  —  150.5  —  4.30 

25.0  —121.3  —  4-86 

15.0  —  77.0  —  5.15  —  6.0 

0.8  10,000  40.0  —  32.4  —  0.8  1 

30.0  —  27.9  —  0.93 

2O.  O  -  2O.  2  -  I.OI  —  1.22  -  O.53 

0.4     On  four  dilutions  there  wa$  no  certain  effect  measured. 

—  o  .  oo  —  o  .  oo 

o  .  2  Since  the  0.4  wt.  N  solution  gave  a  value  which  was  too  small  to  be  measured, 
no  dilutions  were  made  on  this  solution.  The  observed  value  may  be  safely  assumed 
tojDe  zero.  The  calculated  value  is  zero. 

TABLE  VIII.  —  HEAT  OF  DILUTION  OF  KC1  :  SrCl2  SOLUTIONS. 

Reversible  molal  heat  of  dil.  L 


Concen- 
tration. 
Wt.  N. 

Solution. 
G. 

Water  of 
dilution. 
Mols. 

Total  heat 
of  dilution. 
Cal. 

Molal  heat 
of  dilution. 

Cal. 

3-2 

IO,OOO 

35-0 

—  375-0 

—  10.66 

25.0 

—  297  .  I 

—11.88 

15.0 

—184.6 

—  12.30 

1.6 

IO,OOO 

35-0 

—  96  .  06 

—2-75 

25.0 

—86.47 

-3-46 

15.0 

—  60  .  80 

—  4.06 

0.8 

10,000 

35-0 

—  18.6 

—  0.53 

25.0 

-16.5 

—0.66 

15.0 

—15  6 

—  i  .04 

Obs.  Calc. 


— 14.0  — 3.9 


—5.2 


—1.3  —o.o 

F.  Discussion. 

Figs.  3  to  7  show  graphically  the  change  of  the  reversible  molal  heat  of 
dilution  with  the  concentration  for  the  various  solutions  studied.  The 
concentrations  expressed  in  terms  of  weight  normality  are  plotted  as 
abscissas,  while  the  heats  of  dilutions  in  calories  per  mol  of  water  of  dilu- 
tion are  plotted  as  ordinates.  Fig.  3  shows  this  for  the  3  single  salts, 
by  means  of  curves,  plotted  to  the  same  scale.  Figs.  4  to  7  show  the 
change  of  the  heat  of  dilution  of  the  various  salt  mixtures  with  their  con- 


centrations.  There  are  2  curves  in  each  of  these  4  figures.  The  one 
labeled  "Obs."  gives  the  curve  as  it  was  observed  experimentally,  while 
the  one  marked  "Calc."  is  plotted  from  data  calculated  on  the  assump- 
tion that  the  heat  of  dilution  of  a  mixed 
salt  solution  is  equal  to  the  sum  of -the 
heats  of  dilution  of  solutions  of  the 
various  constituents  at  concentrations 
equivalent  to  their  concentrations  in  the 
mixed  solution. 

It  will  be  noted  at  once  that,  without 
exception,  the  observed  values  lie  on  a 
curve  which,  except  at  low  concentra- 
tions, is  significantly  lower  than  the 
curve  for  the  calculated  values.  This 
holds  even  in  the  case  of  the  mixed 
sodium  and  potassium  salts  where  one 
might  expect  the  least  deviation  from  the 
thfcon'  calculated  values;  and  is  in  harmony  with 
centration  for  solution  of  the  salts  the  conclusion1  that  the  ion-fraction  of 
SrCl,,  NaCl  and  KG  Qne  of  ^  metallic  constituents  increases 

with  increasing  total  salt  concentration,  since  the  two  curves,  which  prac- 
tically coincide  at  low  concentrations,  diverge  more  and  more  as  the  total 
salt  concentration  increases.  The  curve,  to  be  sure,  does  not  indicate 
which  of  the  ion-fractions  increases. 

There  seems  to  be  no  simple  relation  between  the  two  curves.  In  the 
case  of  the  mixture  NaCl  :  1/2  SrCls  the  divergence  is  even  less  than  in 
the  case  of  NaCl  :  KC1  where  the  least  divergence  might  be  expected. 
These  experimental  curves,  then,  seem  to  be  influenced  by  3  factors. 
There  are  the  specific  effects  of  the  two  salt  components,  and  there  is  also 
the  very  apparent  effect  of  a  third  species  of  molecular  aggregate,  in  all 
probability  a  molecular  complex  of  the  two  salts  with  varying  amount 
of  water.  The  concentration  of  these  complexes,  in  equilibrium  with 
their  simple  components,  will  be  low  at  low  total  salt  concentrations, 
and  the  specific  effect  on  the  curve  will  be  slight  in  that  region  so  that  the 
two  curves  should  tend  to  come  together  at  low  concentrations.  This  is, 
as  is  observed,  the  case.  As  the  total  salt  concentration  increases,  the 
concentration  of  these  complexes  correspondingly  increases  and  the  curve 
is  given  a  component  of  slope  characteristic  of  them  and  depending  on 
two  things;  namely,  their  individual  "heats  of  dilution"  at  the  concentra- 
tion at  which  they  occur,  which  will  depend  primarily  perhaps  on  their 
heats  of  formation;  and  the  rate  of  change  of  their  concentration  with 

1  Smith  and  Ball,  J.  Am.  Chem.  Soc.,  39,  179  (1917). 


i6 


the  total  salt  concentration,  or,  in  other  words,  the  value  of  their  equi- 
librium constant. 

Thus,  if  the  value  of  k  in  the  expression 
[(Kd),  .  (NaCl)y] 

(KCl),(NaCly) 

is  large,  and  if  the  complex  [(KC1)*  .  (NaCl)y]  has  a  high  heat  of  dilu- 
tion we  would  expect  the  slope  of  the  experimental  curve  to  be  widely 
divergent  from  that  of  the  calculated  curve,  since  a  substance  of  high  heat 

0/23  0/23 


-30 


Fig.  4. — Reversible  molal  heat  of  dilution 
as  a  function  of  the  concentration  for  the 
mixed  salt  solution  NaClrKCl. 

Fig.  6. — Reversible  molal  heat  of  dilution 
as  a  function  of  the  concentration  for  the 
mixed  salt  solution  KCl:i/2  SrCl2. 


Fig.  5. — Reversible  molal  heat  of  dilu- 
tion as  a  function  of  the  concentration  for 
the  mixed  salt  solution  NaCl:i/2  SrCl2. 

Fig.  7. — Reversible  molal  heat  of  dilu- 
tion as  a  function  of  the  concentration  for 
the  mixed  salt  solution  KCl:SrCl2. 


of  dilution  is  being  rapidly  produced  with  increasing  total  salt  concentra- 
tion.    If  the  value  of  k  is  small  the  curves  will  diverge  less  rapidly. 

Table  IX  gives  the  results  of  a  short  series  of  experiments  in  which  very 
large  quantities  of  water  of  dilution,  5.555  mols  E^O  and  10,000  g.  of 


17 

solution,  were  used.  The  same  tendencies  will  be  noticed  as  before.  In 
each  of  the  3  cases  of  mixed  salt  solutions  the  observed  value  of  the 
molal  heat  effect  is  greater  (negatively)  than  the  calculated  value,  a  rela- 
tionship which  agrees  with  those  brought  out  in  the  curves. 

IX. 


Salt. 

SrCl2  

Cone. 

3.2  wt.  N 

KC1  

32  wt.  N 

NaCl 

3  2  wt   N 

NaCl  :  KC1  

3.2  wt.  N 

NaCl  :  1/2  SrCl2  
KC1  :  1/2  SrCl9.. 

3.2  wt.  N 

1  .  2   Wt.   N 

The  assumption  of  these  complexes  is  not  out  of  harmony  with  experi- 
mental data.  The  substances  2KCl.SrCl2  and  2NaCl.SrCl2  have  both 
been  prepared  and  isolated1  and  ions  of  the  type  (SrCU)""  and  (BaCU)" 
have  been  referred  to  as  probably  existing  in  solution.2  Indeed  it  seems 
probable  that  there  are  very  few  types  of  compounds  which  do  not  tend 
to  form  "higher  order  compounds."3 

As  was  stated  in  the  introduction,  according  to  Nernst  the  existence  of 
a  measurable  heat  of  dilution  seems  due  to  the  existence  of  complexes 
which  are  formed  or  decomposed  with  dilution.4 

The  thermodynamic  expression  for  the  reversible  molal  heat  of  dilu- 
tion, LD,  is 

=    RT2dlnp/Po 
dT 

where  p  is  the  vapor  pressure  of  the  solution,  and  p0  is  the  vapor  pressure 
of  the  pure  solvent  at  the  same  temperature.  For  a  negative  value  of  LD, 
as  in  the  case  of  potassium  and  sodium  chlorides,  the  equation  tells  us  that 
the  ratio  p/p0  decreases  with  the  temperature.  Thus,  if  p/p0  de- 
creases with  increasing  temperature,  it  means  that  p  increases  more 
slowly  than  p0  with  the  temperature,  and  from  Raoult's  law  this  would 
indicate  that  at  higher  temperatures  there  is  an  increase  in  the  degree  of 
ionization  of  the  salt.  A.  A.  Noyes5  found  experimentally,  however,  that 
for  salts  of  this  type  the  opposite  was  true,  namely,  that  the  degree  of 
ionization  actually  decreased  with  the  temperature.  There  must,  there- 
fore, be  some  factor  which  aids  in  determining  what  this  value  shall  be, 
other  than  simple  ionization.  The  heats  of  ionization  can  be  obtained 
from  a  knowledge  of  the  rate  of  change  of  the  degree  of  ionization  with 
the  temperature,  from  the  relation 

1  Berthelot  and  Ilosvay,  Ann.  chim.,  [5]  29,  318  (1885). 

2  Noyes  and  Falk,  /.  Am.  Chem.  Soc.,  33,  1455  (1911). 

3  A.  Werner,  Neuere  Anschanungen  a.  d.  Gebiete  d.  Anorg.  Chemie  (1913). 

4  Loc.  cit. 

5  A.  A.  Noyes,  Carnegie  Inst.  Pub.,  63,  339  (1907). 


i8 
din  K         Q 


dT  RT2' 

The  values  calculated  from  this  relationship,  however,  do  not  seem  to 
agree  with  those  observed.  For  instance,  Arrhenius  gives  the  energy 
equation  for  the  ionization  of  dissolved  potassium  chloride1  as 

KC1  =  K+  +  Cl-  +  362  cal., 

whereas,  when  calculated,  the  value  of  the  heat  of  ionization  is  found  to  be 
—  2,000  calories.  According  to  Senter,  "it  seems  that  the  process  of  ion- 
ization must  be  attended  by  some  exothermic  reaction  which  more  than 
compensates  for  the  heat  presumably  absorbed  in  splitting  up  the  mole- 
cules." Van  der  Waals,2  as  well  as  Werner,  has  suggested  that  ioniza- 
tion in  aqueous  solution  is  essentially  a  hydration  process  and  thus  the 
energy  necessary  for  its  completion  may  come  from  the  combination  be- 
tween the  ions  and  water.  The  heats  of  ionization  are  small  in  com- 
parison with  the  heats  of  hydration.  Thomsen3  has  found  values  as  high 
as  8,000  calories  per  mol  of  water  combining  to  form  a  hydrate.  Of  the 
two  effects,  therefore,  this  one  would  predominate.  The  order  of  magni- 
tude of  the  heats  of  formation  of  higher  order  complexes  of  mixed  salts 
is  also  great  enough  to  overshadow  any  ionization  effect.  A  few  examples 
are  taken  from  Pattison  Muir's,  "Elements  of  Thermal  Chemistry,"  Ap- 
pendix I: 

SiF4(aq)  +  2KF(aq)  =  K2SiF6(aq)  +  23,000  cal. 

NaF  +  HF  =  NaHF2  +  17,000  cal. 

NH3  +  HC1  =  NH4C1  +  42,000  cal. 

AuBr3(aq)  +  HBr(aq)  =  HAuBr4(aq)  +  7,700  cal. 
These  heats  are  all  positive.  Now  it  will  be  noted  in  the  curves  in 
Figs.  4  to  7  that  the  deviations  of  the  observed  values  from  those  calculated 
are  always  toward  a  larger  negative  heat.  That  is,  with  dilution,  the 
complexes  existing  in  the  solution  are  broken  up  with  the  absorption  of 
heat. 

G.   Summary. 

1.  The  reversible  molal  heat  of  dilution  has  been  determined  for  solu- 
tions of  the  single  salts,  sodium,  potassium  and  strontium  chlorides  at 
various  concentrations  ranging  from  3.2  wt.  N  to  0.02  wt.  N,  and  also  for 
solutions  of  the  mixed  salts  NaCl  :  KC1,  NaCl  :  l/&rC\*  KC1  :  l/i  SrCl2, 
and  KC1  :  SrCk  for  the  above-mentioned  range  of  concentration. 

2.  The  heats  of  dilution  of  sodium  and  potassium  chlorides  are  nega- 
tive.    This  fact  in  the  light  of  the  equation 


dT 

1  Senter,  "Outlines  of  Physical  Chemistry,"  p.  344. 

2  Van  der  Waals,  Z.  physik.  Chem.,  8,  215  (1891). 

3  Pattison  Muir,  "Elements  of  Thermal  Chemistry,"  p.  167. 


19 

in  which  L#  is  the  molal  heat  of  dilution,  indicates  an  increase  in  the  de- 
gree of  ionization  with  the  temperature,  contrary  to  the  experimental 
results  of  A.  A.  Noyes,  unless  explained  on  the  basis  of  the  decomposi- 
tion with  dilution,  of  complexes  existing  in  the  solution. 

3.  The  heats  of  dilution  for  the  solutions  of  the  mixed  salts  bear  no 
simple  additive  relation  to  the  heat  effects  of  the  single  components  at 
equivalent  concentrations. 

4.  The  results  have  been  explained  on  the  basis  of  the  conception  of 
higher  order  compounds  as  put  forth  by  A.  Werner. 


BIOGRAPHY. 

The  writer  of  this  thesis  received  his  early  education  in  the  public 
schools  of  Eldon,  Missouri,  and  St.  Louis,  Missouri.  He  entered  Leland 
Stanford  Junior  University  in  the  autumn  of  1912  and  graduated  with  the 
degree  of  Bachelor  of  Arts  in  Chemistry  in  the  spring  of  1915.  The  follow- 
ing year,  1916,  he  received  the  degree  of  Master  of  Arts.  The  thesis  con- 
sisted of  "A  Study  of  the  Basic  Sulfates  of  Copper"  (/.  Am.  Ghent  Soc., 
38,  1947  (1916)),  and  was  carried  out  under  the  direction  of  Prof.  S.  W. 
Young.  During  the  academic  year  1914-1915  he  held  the  position  of 
Teaching  Assistant  in  Chemistry  in  Stanford  University,  and  during  1915- 
1916  that  of  Lecture  Preparation  Assistant,  and  Assistant  in  Toxicology 
and  Medical  Organic,  respectively. 

In  1916  he  entered  the  graduate  school  of  the  University  of  Illinois  as  a 
Fellow  in  Chemistry,  and  received  in  June,  1917,  the  degree  of  Master  of 
Science.  The  thesis  was  on  the  "Mechanism  of  Colloidal  Behavior.  I. 
The  Swelling  of  Fibrin  in  Acids"  (J.  Am.  Ckem,  Soc.,  40,  264  (1918)),  and 
was  carried  out  under  the  direction  of  Major  Richard  C.  Tolman.  During 
the  academic  year  1917-1918  he  held  the  position  of  Research  and  Teach- 
ing Assistant  in  Physical  Chemistry  in  the  University  of  Illinois,  and 
during  1918-1919  that  of  Assistant  in  Chemistry  at  the  same  place.  He 
is  a  member  of  Phi  Beta  Kappa,  Sigma  Xi,  Phi  Lambda  Upsilon,  and 
Alpha  Chi  Sigma. 


14  DAY  USE 

RETURN  TO  DESK  FROM  WHICH  BORROWED 
LOAN  DEPT. 

This  book  is  due  on  the  last  date  stamped  below,  or 

on  the  date  to  which  renewed. 
Renewed  books  are  subject  to  immediate  recall. 


14fer'58RHp 

REC'D  LD 

FEB281958 

16May'6lM»r 

Ri-^'D  LD 

MAY  4.     1961 





. 



21A-50m-8,'57 
(C8481slO)476B 


University  of  California 
.    Berkeley 


Gaylord  Bros. 

Makers 

Syracuse,  N.  Y. 
PAT.  JAN.  2 1,1 908 


464191 


UNIVER5ITY  OF  CALIFORNIA  LIBRARY 


